How to wedge in, or extrude triangularly?
You can push your top face down, add a loop cut, then extrude one face up. Then, you can simply drag the remaining edge to the same height.



You can also skip the first step, and simply add a loopcut. Select the face on the right, press extrude, and LMB. Then, pull up that face and the other edge.



This one is a little bit tricky, but uses the same method. Add a loopcut, Select the face on the left, press extrude, then click. Then, with the vertex selection mode active, press Ctrl+I to select evreything but the vertices connected to that face. Then, deselect all vertices except for the two in the middle. You can now move them down. DO note that you may want to also press W - Remove doubles, as this method will have two vertices in the same spot.